The Syllogisms in Paul of Venice’s Logica Magna Sara L. Uckelman s.l.uckelman@durham.ac.uk @SaraLUckelman Durham University British Society for History of Philosophy Sheffield, England 07 Apr 2017 Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 1 / 23
Background Logica Magna of Paul of Venice (?) Published 1499, Venice. Tract II, Chapter 13: chapter on syllogisms. Equal parts rehearsal of orthodox Aristotelian syllogisms and systematization of non-Aristotelian syllogisms. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 2 / 23
Contents Definition of a syllogism ◮ Regular vs. irregular ◮ Direct vs. indirect ◮ Exceptions to the ‘standard’ definition The six moods of the first figure: Barbara, Celarent, Darii, Ferio, Fapesmo, Fresiso The four moods of the second figure: Cesare, Camestres, Festino, Baroco. The six moods of the third figure: Darapti, Felapton, Dissamis, Datisi, Brocardo, Ferison. On irregular syllogisms. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 3 / 23
Things to notice Regular vs. irregular, direct vs. indirect. Modal syllogisms scattered throughout. . . but they are not “ordinary” modal syllogisms. Conditional arguments treated as “syllogisms”. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 4 / 23
What is a syllogism? A syllogism is a speech in which from whatever is posited and conceded it is necessary that another arises through the same which are posited and conceded. This definition is taken from the Philosopher in the first [book] of the Prior [Analytics] which is obvious in itself: for this reason, in this I am unwilling to expand [on this] but, having truncated, I divide ‘syllogism’ into regular and irregular, of which the latter is spoken of in its place. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 5 / 23
Direct vs. indirect conclusions It is a direct conclusion whenever the major extreme or something matching it is predicated of the minor extreme or something matching it in the conclusion, just as here: “Every man is an animal, you are a man, therefore, you are an animal”. An indirect conclusion is when the minor extreme or something matching it is predicated of the major extreme or something matching it in the conclusion, as in the example: “Every man is animal, Socrates is a man, therefore an animal is Socrates”. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 6 / 23
Regular syllogisms Regular syllogisms have three figures containing moods, any argument in which proves to be formal. In the first figure it is required that the subject in the major [premise] be, either implicitly or explicitly, matchable to the predicate of the minor.. . . For example, this syllogism is valid: “Every human is animal, Socrates is a human, therefore Socrates is an animal”, and [it is] in the first figure, because the subject of the major is matchable to the predicate of the minor through every sort of similitude and subordination with the required supposition because in both places ‘human’ stands for either one or the other gender only, [and] although it happens differently in different cases, it doesn’t have to cause variation in the syllogism. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 7 / 23
Premises without implicit or explicit quantity Nothing is a syllogism unless implicitly or explicitly all of the premises are of some quantity. Thus, none of the following syllogisms are valid, or in the first figure: Exceptive Every running thing is an animal, every man except for Socrates is running, therefore every man except for Socrates is an animal . Exclusive Every man is a substance, only animal is man, therefore only animal is a substance . Exponible Every man begins to be Socrates, Socrates is a man, therefore Socrates begins to be Socrates . Modal Of necessity every man is an animal, Socrates is a man, therefore of necessity Socrates is a animal Every creating thing is contingently God, but every first cause is creating, therefore every first cause is contingently God . Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 8 / 23
A few corollaries 1 The first figure derives every genus of proposition, affirmative and negative, universal, particular, indefinite, and singular. 2 In the four moods of the first figure, if the minor is negative, nothing follows, otherwise from a truth a falsehood is concluded. 3 In these moods, when the major is particular or indefinite, nothing follows, as in: “Something risible is Socrates, every man is risible, therefore every man is Socrates”. And if it is said that this follows correctly: “Something risible is an animal, every man is risible, therefore every man is an animal”, it is said that this is true not in virtue of the syllogism but in virtue of this formal consequence: “Every man is risible, therefore every man is an animal”. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 9 / 23
Matchability And I call the subject of the major matchable to the predicate of the minor when it is either altogether similar to it, or to a principal part of the same owing to the supposition, or is dissimilar to [a part] of the same thing in the first way in similar circumstances. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 10 / 23
Supposition It is necessary for the terms of the conclusion to supposit precisely for the same thing or things and for that reason this is not a consequence is not valid: “Every animal is a substance, every man is an animal, therefore some [quilibet] man is a substance”. Neither does this particular, “Some [aliquis] man is a substance”, follow from these premises. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 11 / 23
Mutation of supposition Although this form is not valid, “No father is the son, every God is the father, therefore no God is the son”, however, it does not follow that this consequence is not good and formal: “No animal is a stone, every man is an animal, therefore no man is a stone”, because in the first consequence general mutation of supposition takes place, because in both places in the major there is personal supposition but in the minor the subject supposits simply for the communal divine essence. But in the other consequence, nowhere is there mutation of supposition. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 12 / 23
Mutation of supposition relating to ampliation Although this consequence is not valid: ‘Nothing which is alive is dead, every horse is something which is alive, therefore no horse is dead’, nevertheless, this is correctly valid: ‘Nothing alive is dead, every horse is alive, therefore no horse is dead’. For the first is not valid because it is not necessary to conclude either the major extreme of the minor or something matchable [to the major] of something matchable [to the minor], because in the minor [premise] ‘horse’ supposits only for present horses, but in the conclusion for present, future, and past horses. For this reason it ought to be concluded from these premises: ‘Therefore no present horse is dead’. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 13 / 23
Two other interesting observations Almost every single example of an invalid syllogism in the first figure involves modal propositions. Many of them involve ‘divine’ terms; and further, there is a special discussion devoted to syllogisms with such terms. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 14 / 23
On irregular syllogisms I call an irregular syllogism that which is put down neither in mood nor in figure but is only one consequence having premises and conclusion with a similitude to a regular figure. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 15 / 23
Examples of irregular syllogisms (1) In the first figure by similitude: Man runs. Socrates is a man. Therefore Socrates runs. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 16 / 23
Examples of irregular syllogisms (1) In the first figure by similitude: Man runs. Socrates is a man. Therefore Socrates runs. Why is this in the first figure “by similitude”? Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 16 / 23
Examples of irregular syllogisms (1) In the first figure by similitude: Man runs. Socrates is a man. Therefore Socrates runs. Why is this in the first figure “by similitude”? because of the location of the terms, because the subject of the major has the required matchable [thing] in the predicate of the minor, and in the conclusion the required matchable [thing] is implicitly predicated of the required matchable [thing]. Sara L. Uckelman (Durham University) The Syllogisms in Paul of Venice’s Logica Magna 07 Apr 2017 16 / 23
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